For the Schrödinger operator \(-\Delta +V(x)\)  on \({\mathbb {R}}^n\)  in any dimensions \(n\ge 1\) , there exists a great number of works are devoted to establish the \(L^p\) -boundedness of the wave operators in last almost thirty years. For instance, Yajima in the seminar work [1]} proved the \(L^p\) -boundedness of wave operators for \(n\ge 3\)  in the regular case. Subsequently, the case \(n=1\)  were studied by Weder [2]} and Artbazar–Yajima [3]} independently and the case \(n=2\)  by Yajima [4]}. Since then later, many further progresses and applications related to the \(L^p\) -boundedness of wave operators have been made for all the regular, zero resonance and zero eigenvalue cases under various conditions on the potential \(V\)  (see [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}, [12]}, [13]}, [14]}, [15]}, [16]}, [17]}, [18]}, [19]}, [20]}, [21]}, [22]}, [23]}, [24]}, [25]}, [26]}, [27]} and references therein). Certainly, these works would play indispensable roles in the studies of higher-order elliptic operators.
